We consider the equations of elastodynamics governing the motion of compressible isentropic inviscid elastic materials. These equations arise as the inviscid limit of the equations of compressible viscoelasticity [1]}, [2]}, [3]} of Oldroyd type [4]}, [5]}. As in [6]}, [7]}, [8]}, [9]}, we restrict ourself to two-dimensional (2D) elastic flows and the special case of Hookean linear elasticity. Then, the elastodynamics equations are written as the following system of conservation laws:
\(\left\lbrace \begin{array}{l}\partial _t\rho +{\rm div}\, (\rho v )=0, \\\partial _t(\rho v ) +{\rm div}\,(\rho v\otimes v ) + {\nabla }p-{\rm div}\,(\rho FF^{\top })=0,\\\partial _t(\rho F_j ) +{\rm div}\,(\rho F_j\otimes v - v\otimes \rho F_j) =0,\quad j=1,2,\end{array}\right.\) 
